Information on Result #1013788

Linear OOA(7102, 7686752, F7, 3, 9) (dual of [(7686752, 3), 23060154, 10]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(726, 5764804, F7, 3, 4) (dual of [(5764804, 3), 17294386, 5]-NRT-code), using
  2. linear OOA(776, 3843376, F7, 3, 9) (dual of [(3843376, 3), 11530052, 10]-NRT-code), using
    • (u, u+v)-construction [i] based on
      1. linear OOA(710, 174, F7, 3, 4) (dual of [(174, 3), 512, 5]-NRT-code), using
        • OA 2-folding and stacking [i] based on linear OA(710, 348, F7, 4) (dual of [348, 338, 5]-code), using
          • construction XX applied to C1 = C([341,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([341,2]) [i] based on
            1. linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
            2. linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
            3. linear OA(710, 342, F7, 4) (dual of [342, 332, 5]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
            4. linear OA(74, 342, F7, 2) (dual of [342, 338, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
            5. linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
            6. linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code) (see above)
      2. linear OOA(766, 3843202, F7, 3, 9) (dual of [(3843202, 3), 11529540, 10]-NRT-code), using
        • trace code [i] based on linear OOA(4933, 1921601, F49, 3, 9) (dual of [(1921601, 3), 5764770, 10]-NRT-code), using
          • OOA 3-folding [i] based on linear OA(4933, 5764803, F49, 9) (dual of [5764803, 5764770, 10]-code), using
            • discarding factors / shortening the dual code based on linear OA(4933, 5764805, F49, 9) (dual of [5764805, 5764772, 10]-code), using
              • construction X applied to Ce(8) ⊂ Ce(7) [i] based on
                1. linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
                2. linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
                3. linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code) (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.